The murder was nearly identical to that of fellow reporter James Foley. Waving a knife toward the camera, the Islamic State fighter says: “Just as your missiles continue to strike our people, our knife will continue to strike the necks of your people.”

After cutting off Sotloff’s head, he is seen next to a British aid worker who is kneeling on the desert floor dressed in an orange jumpsuit.

The hostage’s name flashes up on screen as his captor warns: “We take this opportunity to warn those governments that enter this evil alliance of America against the Islamic State to back off and leave our people alone.”

Reacting to the video on Tuesday night, a visibly shocked David Cameron said: “It is an absolutely disgusting and despicable act. This is a despicable and barbaric murder.

“ISIL terrorists speak for no religion. They threaten Syrians, Iraqis, Americans and British people alike and make no distinction between Muslims, Christians or any other faith.”

The prime minister will chair a meeting of Cobra, the government’s emergency planning committee, on Wednesday. The threat to Britain came just a day after Cameron warned the UK could join US bomb attacks on Islamic State forces that are terrorising northern Iraq.

He has also announced measures to combat the danger from British jihadists returning from fighting in the Middle East.

The killer’s identity is known to the security services, but it is not now thought to be Abdel-Majed Abdel Bary, the so-called hip-hop jihadist from West London.

Last week, Sotloff’s mother made a desperate appeal to her son’s captors to spare his life. Shirley Sotloff begged the terror group’s leader, Abu Bakr al-Baghdadi, for clemency, saying: “My son is in your hands.

“As a mother I ask your justice to be merciful and not punish my son for matters he has no control over. I ask you to use your authority to spare his life. Steven has no control over the actions of the US government. He’s an innocent journalist.”

In the video, titled A Second Message To America, the British jihadi speaks in a London accent and appears to be the same left-handed man who killed Foley a fortnight ago.

He wears black, has a weapon strapped under his arm and the black flag of the Islamic State can be seen waving in the background.

Moments before his killing, Sotloff, 31, is made to read a propaganda statement. “I’m sure you know exactly who I am by now and why I am appearing,” he is made to say.

“Obama, your foreign policy of intervention in Iraq was supposed to be for preservation of American lives and interests, so why is it that I am paying the price of your interference with my life?”

Barack Obama was in the White House when the video was released, preparing for a trip to Estonia and then Wales, where he will attend a Nato summit.

His chief spokesman Josh Earnest said: “Our thoughts and prayers, first and foremost, are with Mr Sotloff and Mr Sotloff’s family and those who worked with him. The United States has dedicated significant time and resources to try to rescue Mr Sotloff.”

Urging Western countries to help Iraq defeat the Islamic State, the country’s outgoing foreign minister, Hoshiyar Zebari, said the video was “an example of savagery and evil”.

“We have a common enemy and the whole world is moving in the right direction to stop this savagery and brutality,” he added.

“The whole world is standing united against IS. They must be defeated so these horrid scenes will not be repeated.”

Sotloff - a freelance reporter for Time and Foreign Policy - was last seen in August 2013. It is believed he was abducted close to the Syrian border with Turkey, near the ancient city of Aleppo. Family members on Tuesday night said his murder was a “horrific tragedy”.

A statement added: “The family knows and is grieving privately. There will be no public comment from the family during this difficult time.”

Foley, 40, worked for organisations including Agence France-Presse and went missing in Syria in 2012. His family described the video released yesterday as “just horrific”.

The killer is one of an estimated 500 Britons who have travelled to Syria and Iraq to join IS. They are said to be among the most vicious of the fanatics and the hostages’ killer may have been selected for heightened global impact because of his nationality. Analysts said IS had “signed its death warrant” with the propaganda videos.

Dr Afzal Ashraf, a terrorism and political violence expert at the Royal United Services Institute think-tank, said: “This is the result of a myth that Osama Bin Laden created that the US would run away whenever it is attacked. They believe that if they carry out this kind of atrocity the US will put its hands up in horror and flee.

“This is a miscalculation. They don’t understand, for some reason, that the opposite will happen. Whatever reluctance Obama feels he will have to overcome because the American people will want justice.

“I think Islamic State’s leadership has effectively signed its death warrant with this act.

“There is a suggestion a UK hostage will be next. That is not going to help Islamic State’s cause one iota because the British government would have to respond. It couldn’t do nothing.

“It will strengthen the case of those in government that want a more robust approach against IS. It will motivate more Western involvement.”

In the Commons, Cameron has been asked directly if he was “open to the idea of direct military participation in air strikes”.

He replied: “I don’t rule anything out. I don’t think we should. We should consider everything.”

A Foreign Office spokesman said: “We are aware of a video which purports to be the murder of a US national and includes a threat to another hostage. We are urgently working to verify the authenticity of the video.”

Cameron added: “My thoughts and prayers are with Mr Sotloff’s family and friends as they deal with this appalling and tragic situation. We have already been working hard to keep British people safe and we will continue to do all we can to protect our country and our people from these barbaric terrorists. I will chair a Cobra meeting to review these latest developments.”

At the request of the Foreign Office, the British hostage in the video is not being named by the Mail.